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3 years ago

14

The sum of a number and two times a smaller number is 62. Three times the bigger number exceeds the smaller number by 116.

1 answer:

g100num [7]3 years ago

8 0

Answer:

the bigger number is 42

the smaller number is 10

Step-by-step explanation:

use algebra to denote:

let x be the bigger number

let y be the smaller number

x+2y=62...(1)

3x-y=116...(2)

x=62-2y...(1a)

substitute

3(62-2y)-y=116

186-6y-y=116

-7y=116-186

-7y=-70

y=-70/-7

y=10

therefore x is:

x=62-2(10)

x=62-20

x=42

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2 years ago

Can please someone help me? The question is in the picture. Thank you

maxonik [38]

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C. $9\pi$

Step-by-step explanation:

We proceed to solve for $x$ by the Pythagorean Theorem:

$(x+1)^{2} = (x-1)^{2} + (2\cdot x - 4)^{2}$ (1)

$x^{2} + 2\cdot x + 1 = (x^{2}-2\cdot x + 1) + (4\cdot x^{2}-16\cdot x + 16)$

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$x_{1} = 4$ , $x_{2} = 1$

A solution of $x$ is considered realistic when the length of every side of the triangle is a not negative number.

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$UV = 2\cdot (4) - 4$

$UV = 4$

$WU = 4 - 1$

$WU = 3$

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The only realistic set of solutions is for $x = 4$ , and the radius of the circle is represented by the line segment $WU$ : $r = 3$

And the area of the circle ( $A$ ) is calculated from the following formula:

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$A = 9\pi$

The correct answer is C.

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